Three-dimensional point to three-dimensional plane (3D-3D) registration is fundamental to computer vision, robotics, object recognition and tracking, image registration, and augmented reality.
The registration problem includes a correspondence problem and a pose estimation problem using the correspondence. Both of these problems are intertwined, and the solution of one depends on the other. As used herein in, the pose is defined by 3D translation and 3D rotation.
Many 3D-3D registration methods are known depending on the representation of the two 3D datasets: 3D points to 3D points, 3D lines to 3D planes, and 3D points to 3D planes. The most common method registers two sets of 3D points. Although approaches such as iterative closest point and its variants exist for this problem, only a few non-iterative methods are known. Other applications involve the registration of 3D lines or points with normals to 3D planes.
Many conventional methods assume that the correspondences are known. Several registration methods focus on solving both the correspondences and pose estimation by casting the correspondence problem as a graph theoretical problem. This is an NP-hard problem, such as a minimum vertex cover, and a maximum clique. Several solutions are known to solve these NP-hard problems using branch and bound techniques.